MIMO receive algorithms

The optimal detection problem in multi-antenna wireless communication systems often reduces to the problem of finding the least-squares solution to a system of linear equations, where the unknown vector is comprised of integers, but the matrix coefficients and the given vector are real-valued. The problem is equivalent to finding the closest lattice point to a given point and is known to be NP-hard. We review the most commonly used solution techniques, and discuss their computational complexity. Among heuristic algorithms, we focus on the nulling and cancelling techniques, and their fast implementations based on linear estimation theory. We then show that an exact method, the sphere decoding algorithm, often has expected complexity implementable in practical systems. We also describe extensions of sphere decoding techniques to receivers that make use of the so-called soft information.